<Emphasis Type="Italic">CR</Emphasis>-Warped Products in Complex Projective Spaces with Compact Holomorphic Factor

A submanifold of a Kaehler manifold is called a CR-warped product if it is the warped product N_T ×_fN of a complex submanifold N_T and a totally real submanifold N. There exist many CR-warped products N_T ×_fN in CP^h+p, h = dim_CN_T and p = dim_RN (see 5, 6]). In contrast, we prove in this article that the situation is quite different if the holomorphic factor N_T is compact. For such CR-wraped products in CP^m (4), we prove the following: (1) The complex dimension m of the ambient space is at least h + p + hp. (2) If m = h + p + hp, then N_T is CP^h(4). We also obtain two geometric inequalities for CR-warped products in CP^m with compact N_T.